Williams Crawford
06/02/2023 · Middle School
Negative Integer Exponents QuICK CneCK Which of the following is an equivalent expression to \( \frac{7^{3}}{25^{-4}} \) with only positive exponents, generated by applying the Property of Negative Integer Exponents? (1 point)
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Step-by-step Solution
To rewrite the expression \( \frac{7^{3}}{25^{-4}} \) with only positive exponents, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^{n}} \).
Starting with the expression:
\[
\frac{7^{3}}{25^{-4}}
\]
We can rewrite \( 25^{-4} \) as \( \frac{1}{25^{4}} \). Therefore, the expression becomes:
\[
\frac{7^{3}}{\frac{1}{25^{4}}}
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
7^{3} \times 25^{4}
\]
Thus, the equivalent expression with only positive exponents is:
\[
7^{3} \cdot 25^{4}
\]
Quick Answer
\( 7^{3} \cdot 25^{4} \)
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